I’m starting the long road to rehab my yard. What do people do when their yard needs two type of grass seeds that can survive in polar opposite conditions?

I am in the process of trying to fix my front lawn. I'm currently just working on killing and removing the weeds and all that. I have a big tree right in the middle of my front which casts a shadow all day beneath that area I endearingly call the circle of life. So basically anything within the green zone lives, within the yellow zone, mostly survives, and the outer rim of the red zone beyond the shade is the circle of weeds and death.

My issue is that when I get to planting seed later this year, how does one reconcile using two types of seeds (e.g. one that can thrive in full shade, the other in full sun) and not having look too different – is there a common approach to this? Yeah I am a newbie at this. I'm in the Northeast (NJ). Any advice is appreciated. Thank you.